El Niño Project (Part 1)

A bunch of Azimuth Project members like to program, so they started the Azimuth Code Project… but now it’s getting more lively! We’re trying to understand and predict the climate phenomenon known as El Niño.

Why? Several reasons:

• It’s the biggest source of variability in the Earth’s climate on times scales between a year and a decade. It causes weather disturbances in many regions, especially near the Pacific Ocean. The last really big one happened in 1997-1998, and we’re waiting for the next.

• It’s hard to predict for more than 6 months in advance. It’s not periodic: it’s a quasi-periodic phenomenon that occurs across the tropical Pacific Ocean every 3 to 7 years.

• It matters for global warming. A lot of heat gets stored in the ocean, and a lot comes back into the atmosphere during an El Niño. So, the average surface air temperature of the Earth may reach a new high when the next El Niño comes.

• In February 2014, a paper in Proceedings of the National Academy of Sciences caused a stir by claiming to be able to predict the next El Niño more than 6 months in advance using ideas from network theory. Moreover, it claimed an El Niño would start in late 2014 with a 75% probability.

• The math involved in this paper is interesting, not too complicated, and maybe we can improve on it. At the very least, it raises a lot of questions worth studying. And it’s connected to network theory, one of the Azimuth Project’s specialties!

We are already hard at work on this project. We could use help from computer programmers, mathematicians, and physicists: there is lots to do! But it makes sense to start by explaining the issues and what we’ve done so far. We’ll do that in a series of posts here.

This first post will not get into many details. Instead, I just want to set the stage with some basic information about El Niño.

El Niño and La Niña

During La Niña years, trade winds blow across the Pacific Ocean from the Americas to Asia in a strong way. So, warm surface water gets pushed toward Asia. Warmer oceans there create more clouds and rain there. The other side of the Pacific gets cooler, so there is less rain in many parts of the Americas.

During El Niño years, trade winds in the tropical Pacific weaken, and blobs of warm surface water move back toward the Americas. So, the eastern part of the Pacific warms up. We generally get more rain in the Americas… but less in Asia.

ENSO

The cycle of El Niños and La Niñas is often called the El Niño/Southern Oscillation or ENSO. Why? Because this cycle is linked to the Southern Oscillation: an oscillation in the difference in air pressure between the eastern and western Pacific:

The top graph shows variations in the water temperature of the tropical eastern Pacific ocean: when it’s hot we have an El Niño. The bottom graph shows the air pressure in Tahiti minus the air pressure in Darwin, Australia — up to a normalization constant, this called the Southern Oscillation Index, or SOI. If you stare at the graphs a while, you’ll see they’re quite strongly correlated—or more precisely, anticorrelated, since one tends to go up when the other goes down. So, remember:

A big negative SOI goes along with an El Niño!

There are other ways besides the SOI to tell if an El Niño is happening. We’ll talk later about these quantities, how they’re defined, how you can get the data online, what we’ve done with this data, and what we want to do.

Is a big El Niño coming?

To conclude, I just want you to watch this short movie. NASA’s Jason-2 satellite has detected blobs of hot water moving east toward America! This has made some scientists—not just those using network theory—suspect a big El Niño is on its way, perhaps a repeat of the one that started in 1997.

On the other hand, on June 17th the National Oceanic and Atmospheric Administation (NOAA) said that trends are now running “counter to typical El Niño development”. So we’ll have to wait and see… and meanwhile, try to predict!

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Looking very good. I have a separate effort going in predicting ENSO and QBO, which have an apparent common underpinning. I am trying to make it as simple and concise as possible but can also volunteer towards a more ambitious route that you are embarking on.

My objective has been toward achieving a simple conceptual or abstract view of ENSO as the primary fluid dynamics component generating climate variability. Having something concise and representative of the actual physics would go a long way to allowing (technical/non-technical/skeptical) sides to help deconstruct what is happening. So what I always search for is the American Journal of Physics equivalent explanation. Yet, as far as I can tell, there is nothing like that to describe ENSO other than the typical phenomenological discussions of geographical winds, waves, etc.

This is also useful in that it can be argued against. In other words, one can formulate an argument why this cannot work. That is often just as effective in gaining a common ground on our understanding. In this case it would explain why the sloshing of liquids that is adequately modeled at a macro-level (large containers filled with fluid) will not work at the super-macro-level of the ocean. So far, I hear the criticism that the Pacific Ocean is much too shallow in relation to its diameter for anything like this model to be applicable.

That is where I am coming from. To create a network of nodes and how they can interoperate is the next logical step. That is exciting and I hope to contribute somehow. I tend to forget about the Azimuth Forum but will start to monitor . Thanks, Paul Pukite

Hi! It would be great if you could contribute, either by joining what we are doing or doing something in parallel and posting it to the Azimuth Blog. Information on how to write Azimuth Blog articles is here:

One of the steps is getting comments from the rest of the Azimuth members, so if you have an idea for an article and aren’t quite sure we’d like it, it’s probably best to start by proposing the idea on the Azimuth Forum.

Consider that besides the Chandler Wobble, tidal periods of 18.6 years, 8.85 years, 6 years, and 16.9 years also exist, and if these get applied to as independent Mathieu periodicities, the fit improves markedly as shown in Figure 3.

but here you write:
If we look at the periods that control lunar tides — the 18.613 year period and the 8.848 period

The Mathieu equation is as described in the book you cited the “angular” part of the Helmholtz equation obtained via a seperation of variables.(I didn’t check this, but I hope it’s right). Your fit looks interesting but is there any way to motivate why the periodic terms for the CBO and Chandler wobble which you introduced here go together with this rather special spatial distribution which enters that Ansatz?

Let me preface that my blog posts are a means for me to track my progress in understanding.

From the literature, there was some indication that the QBO could be influencing ENSO directly. The downwelling winds from the QBO could be agitating the ocean waters to stimulate the ENSO. However, I could not get a good fit using QBO as a forcing function directly. The best I could do was use a few principal components (i.e. Fourier series factors) from the QBO and tweak those slightly. This should inform us that perhaps that instead of QBO acting as a direct stimulus to ENSO that there is a common factor to both QBO and ENSO. The two principal periodic components of 2.3 years and 2.7 years that I found underlying QBO correspond closely to the folded or aliased frequencies for the synodic/sidereal lunar monthly periods and draconic or nodal monthly periods, respectively. So I am currently leaning toward a lunar tidal influence as a forcing function to both QBO and ENSO. Note that this is not a well accepted idea, as most theories for QBO follow Richard Lindzen’s original idea for intrinsic atmospheric properties leading to emergent oscillations.

BTW, the various combinations of sidereal, draconic, and anomalistic lunar months lead to the 18.6, 8.85, and 6 year repeat periods. These are beat frequencies of the monthly periods interfering with each other.

As for the Mathieu equation, there are two schools of thought where it might apply. On a literature search the first application I found, dating back to 1929 and earlier, was as a spatio-temporal approximation to an elliptical basin. This leads to the same separable equations as an elliptical drumhead.
The second much more recent application is to describe the sloshing of fluid in an excited volume, such as in a fluid-filled tank in motion. The following paper is what I have been working from:
[1]J. B. Frandsen, “Sloshing motions in excited tanks,” Journal of Computational Physics, vol. 196, no. 1, pp. 53–87, 2004.

This is a discovery process for me, and if you read my blog posts you will see some dead ends and false starts. The Chandler wobble connection may be a dead end, but it also may be useful along with all the angular momentum LOD (length of day) measurements to pin down the origins of the forcing.

That’s why I am excited to see what I can contribute and get on the correct path.

[…] There’s also a good article on El Niño and La Niña which for whatever reason didn’t get the label of Beyond Discovery. [As I write this (June 2014), there's a recent (February 2014) paper in PNAS claiming three-in-four likelihood of return of El Niño by the end of this year; having predicted it more than 6 months in advance would be very exciting if it does happen. John Baez writes more at Azimuth.] […]

So in particular the Kessler image is showing an El nino peak around 1978 (the exact year is hardly visible), all other peaks until the 1940’s are smaller (in the negative sense,i.e. closer to 0) than this peak. However the NOAA image shows no peak around this year but only one in 1974, but a couple of other peaks until the 1950’s. Frankly I find the Index diagram better than this annual bar diagram form NOAA, but the NOAA image is an offical release. Is there an official index diagram somewhere?

Paul Pukite and Graham Jones have been developing a characterization of the ENSO which involves a physical sloshing model. They’re seeking help in model evaluation and assessment of time series. I’ve decided to pitch in. This is another Azimuth Project effort. See the following links:

How To Write Math Here:

You need the word 'latex' right after the first dollar sign, and it needs a space after it. Double dollar signs don't work, and other limitations apply, some described here. You can't preview comments here, but I'm happy to fix errors.